Out of all "possible" final scores (0<R<3*n) for a team, participating in N games, how many final results cannot be achieved?
| See The Solution | Submitted by Ady TZIDON |
| Rating: 4.0000 (1 votes) |
Not achieved (spoiler)
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 | Comment 1 of 5 |
(I want to say the answer is zero since if a score cannot be achieved it is not possible. But I know this isn't what you mean. I don't remember this problem from the queue or I'd have suggested a rewrite.)
The answer is 1. For N games the only unachievable score is 3N-1.
Numbers of the form 3m can be (W,L,D) = (m,N-m,0)
Numbers of the form 3m+1 can be (m,N-m-1,1)
Numbers of the form 3m+2 can be (m,N-m-2,2) except where
there is only 1 non-win. In that case there cannot be 2 draws.
The answer is 1. For N games the only unachievable score is 3N-1.
Numbers of the form 3m can be (W,L,D) = (m,N-m,0)
Numbers of the form 3m+1 can be (m,N-m-1,1)
Numbers of the form 3m+2 can be (m,N-m-2,2) except where
there is only 1 non-win. In that case there cannot be 2 draws.
| Posted by Jer on 2013-04-03 11:32:42 |
